180 Days of Ideas for Discussion in Math Class. (as of 9July2014, we're in overtime!)

My TI-89 tells me the answer is a sideways 8. What does that mean? Is this thing broken?

You got to figure out the pattern: 3^1 =3, 3^2 = 9, 3^3 = 273^4 = 813^5 =243units digit goes 3, 9, 7, 1, 3, ...So, how many groups of four is that?

It is 3^ 27 which would end in 7, no?

it's 3^(3^3^3), which can be rewritten as 3^(27^3).27^3 = 19683 and 19683 / 4 = 4920.75 OR 19683 mod 4 = 3Either way of thinking gets you that we're at the third spot in the cycle, units digit is 7.

My TI-89 tells me the answer is a sideways 8. What does that mean? Is this thing broken?

ReplyDeleteYou got to figure out the pattern:

ReplyDelete3^1 =3,

3^2 = 9,

3^3 = 27

3^4 = 81

3^5 =243

units digit goes 3, 9, 7, 1, 3, ...

So, how many groups of four is that?

It is 3^ 27 which would end in 7, no?

ReplyDeleteit's 3^(3^3^3), which can be rewritten as 3^(27^3).

ReplyDelete27^3 = 19683

and 19683 / 4 = 4920.75 OR 19683 mod 4 = 3

Either way of thinking gets you that we're at the third spot in the cycle, units digit is 7.